Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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Intraocular Lens
The invention concerns an intraocular lens (IOL) and a method of
determining the imaging properties of intraocular lenses.
Lenses of that kind are known. The topology of conventional
intraocular lenses generally involves spherical curved surfaces whose
imaging properties however are not ideally suited to producing an image on
the retina of the human eye. Known methods of determining the imaging
properties of intraocular lenses therefore presuppose basically spherically
curved surfaces.
The object of the invention is to provide an intraocular lens whose
imaging properties produce an image of improved quality on the retina. A
further object of the invention is to provide a method of determining the
imaging properties of the intraocular lens, which method provides reliable
results independently of the topological nature of the lens.
According to the invention that object is attained by an intraocular
lens with negative spherical aberration. Conventional, spherically curved
intraocular lenses of positive refractive power have a positive spherical
aberration, that is to say they refract an incoming wave with a plane wave
front into an outgoing wave with an elliptically oblongly curved wave front.
The focus of such a lens is accordingly not punctiform. In comparison the
intraocular lens according to the invention is preferably of such a
configuration that, in the environment of immersion medium, in particular
the in vivo environment (refractive index 1.336) in the eye it refracts an
incoming wave with an elliptically oblongly curved wave front into an
outgoing wave with a wave front which is substantially spherical. In that
way the imaging properties of the cornea of the eye, which is in front of the
IOL, are better taken into consideration and the effect is that more
accurate focusing on the retina is possible.
Such imaging properties are preferably achieved by the refractive
index and the curvature of the lens surfaces being so selected that the lens
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at the centre has a refractive power D of greater than or equal to +3
dioptres (dpt) in the immersion medium and that in the environment of air
an incoming wave with a substantially plane wave front is refracted into an
outgoing wave with a hyperbolic wave front.
The shape of the curvature of the wave fronts and also the curvature
of the lens surfaces can be described by the following function:
y2 = px - (1 + asph)x2 (1)
wherein x coincides with the direction of light propagation or the lens
thickness, y specifies the direction perpendicular thereto, radially outwardly
with respect to the lens centre, p is any parameter and asph is so-called
asphericity, that is to say a measurement in respect of the deviation of the
curvature of the lens surface from a spherical shape. The shape of the lens
surface or wave front is shown in section for different asphericities in
Figure
1. With an asphericity of greater than 0 the equation accordingly describes
an ellipse whose minor axis in the x-direction (illustrated on an extended
scale) is less than that in the y-direction (oblong). If the asphericity is
equal to 0, a circle is described. If it is between 0 and -1 (in each case
excluding the limit values), an ellipse is described, whose major axis in the
x-direction is greater than that in the y-direction (prolong). If the
asphericity is -1 then equation (1) describes a parabola and if its value is
less than -1 it then describes a hyperbola.
Preferably the hyperbolic wave front of a wave produced from an
incoming plane wave by the lens according to the invention has an
asphericity (asphouT) of less than or equal to -1. Also the intraocular lens
z5 preferably has at least one convexly curved surface whose curvature is of
an asphericity (asph~) of less than or equal to -1.
The invention is described in greater detail hereinafter by means of
embodiments by way of example with reference to the Figures in which:
Figure 1 shows a view of the curvature of a curve described by
equation (1) for various asphericity values,
Figure 2 shows a diagram of the asphericity of an outgoing wave for
various topographical asphericities of the cornea with a corneal refractive
power at the centre of 40 dioptres,
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Figure 3 shows a diagram of the asphericity of an outgoing wave for
various topographical asphericities of the cornea with a corneal refractive
power at the centre of 50 dioptres,
Figure 4 shows a diagram of the negative asphericity of the surface
of a first embodiment of the IOL according to the invention for the
conversion of a spherical wave into another spherical wave and the
negative asphericity of an outgoing wave measured in air and in the
immersion medium in each case in dependence on the refractive power of
the lens,
1o Figure 5 shows a diagram of the negative asphericity of the surface
of a second embodiment of the IOL according to the invention for the
conversion of an aspherical wave into a spherical wave and the negative
asphericity of an outgoing wave measured in air and in the immersion
medium in each case in dependence on the refractive power of the lens,
Figure 6 is a diagrammatic view of a measuring apparatus for
determining the waveform of the outgoing wave refracted by an IOL with
incoming radiation of plane waves,
Figure 7 shows a diagrammatic cross-section through a third
embodiment of the IOL according to the invention,
Figure 8 shows the wave front of an outgoing wave from the IOL
shown in Figure 7 in comparison with an outgoing wave from a lens with
spherical surfaces measured in air, and
Figure 9 shows the wave front of an outgoing wave from the IOL
shown in Figure 7 in comparison with an outgoing wave from a lens with
spherical surfaces measured in the immersion medium.
The imaging conditions taken into account in relation to the IOL
according to the invention, in the human eye, are investigated hereinafter.
As is known the cornea has a refractive index of about 1.37,
topographically it essentially represents an aspheroidal dish. It has a
negligibly slight influence on refraction of an incoming wave. Refraction of
the incident light depends rather on the one hand on the curvature which is
predetermined by the topography of the cornea but on the other hand on
the refractive index of the immersion medium behind the cornea (aqueous
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humour). As is known, that has a refractive index of 1.336. The topography
of the cornea is characterised by the asphericity (asph~), for which the
literature specifies values of asph~ _ -0.26 ~ 0.18 (Kiely et al, in G Smith
et al, Vision Research 41, 2001, 235-43) and asph~ _ -0.18 ~ 0.15 (Guillon
et al, loc. cit.). In accordance with those literature values it can be
assumed that the cornea of the human eye is generally elliptically curved.
For the following considerations, a value range of asph~ _ -0.56 to 0 is
therefore assumed for the asphericity of the cornea, in order to ensure that
practically all human cornea asphericities occurring in nature are embraced.
i0 In that respect it is to be observed that the upper limit value (asph~ = 0)
corresponds to a cornea with spherical curvature.
In addition the topography of the cornea is characterised by its
surface refractive power at the centre point, that is to say on the optical
axis. A range of 40 to 50 dioptres (dpt) is assumed for that purpose,
whereby the range of the surface refractive power of the cornea, which
actually occurs in nature and which in accordance with knowledge at the
present time is at 43 dpt as an average value, is masked both towards
higher and also lower values.
Figures 2 and 3 show the asphericity (asphlN) of a wave refracted by
the cornea or the immersion medium, on the incidence of a plane wave,
that is to say a wave with a plane wave front, like for example light which
is emitted by a point at an infinitely far distance. That depends on the
topographical asphericity of the cornea and the spacing of the apex of the
wave front from the apex of the cornea (abscissa value). The spacing
between the centre of the intraocular lens and the front apex point of the
cornea in the human eye, which is between a minimum of 3 mm and a
maximum of 6 mm, is taken as the basis for the range of that value. Figure
2 specifies the conditions in the case of a cornea with a central surface
refractive power of 40 dpt. It can be seen therefrom that the asphericity of
the refracted wave front which impinges on the intraocular lens ranges
between the limit value asphIN = 0 with a topographical asphericity of the
cornea asph~ _ -0.56 and the limit value asphIN = 10.8 with a topographical
asphericity asph~ = 0. On the basis of a central surface refractive power of
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the cornea of 50 dpt, see Figure 3, the asphericity of the refracted wave
front asphlN impinging on the intraocular lens is between 0 and +11.4.
Overall therefore it can be established that the asphericity of that wave
front is always in the last-mentioned range, and the wave front is therefore
5 either spherical (asphIN = 0) or otherwise always elliptically oblongly
curved
(asphIN > 0). In other words the cornea has a positive spherical aberration
as it refracts the beams at the edge more greatly than those at the centre.
Based on that realisation therefore an IOL with negative spherical
aberration is required in order to refract the aspherical wave coming from
1o the cornea so as to achieve improved image formation on the retina of the
eye.
Preferably the IOL according to the invention is so designed that, in
the environment of immersion medium, an incoming wave with an
elliptically oblongly curved wave front is refracted into an outgoing wave
with a substantially spherical wave front, wherein the refractive power of
the IOL is to be so selected in dependence on the eye of the patient that
the centre of the outgoing waves is on the retina of the eye.
The IOL according to the invention can assume various
configurations: in accordance with a first embodiment, at its centre, in the
2o environment of the immersion medium, it has a refractive power DI of at
least +3 dpt and the refractive power decreases towards the edge of the
lens. In addition by way of example a refractive index of 1.46, a lens
diameter of 6 . mm and an axis-parallel edge thickness of 0.25 mm is
assumed to apply.
Figure 4 shows the required negative asphericity of the surfaces
(asph~) of a first, biconvex, symmetrical embodiment of the IOL according
to the invention for the conversion of an incoming wave with a spherical
wave front (asphlN - 0, that is to say for the extreme case of a
topographical asphericity of the cornea, which is to be expected as a
minimum, of -0.56) into an outgoing wave with an also spherical wave
front (asphouT = 0). The asphericity of the surfaces of the IOL depends on
the central surface refractive power of the IOL in the immersion medium.
The configuration is shown in the lower curve (open circles).
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In addition Figure 4 (open triangles) shows the configuration of the
negative asphericity of the wave front of the outgoing wave which is
produced by a corresponding IOL in the immersion medium if the incoming
wave has a plane wave front. The upper curve in Figure 4 (open squares)
shows the negative asphericity of the wave front of an outgoing wave which
is produced by the same lens measured in air when a wave with a plane
wave front is incident.
Figure 5 shows in a corresponding manner the negative asphericity
of the surfaces of a biconvex, symmetrical IOL (open circles) asph~, which
is suitable for refracting an incoming aspherical wave with the maximum
asphericity to be expected in the human eye, asphIN = 11.4, into a wave
with a spherical wave front. The wave front of a plane incoming wave
refracted by such a lens is shown in the two curves thereabove, namely for
measurement in air (open triangles) and measurement in the immersion
medium (open squares).
It is to be seen from Figures 4 and 5 that the topographical
asphericities of the refractive surfaces of the intraocular lens according to
the invention at any event assume negative values of less than -1 and the
surfaces are therefore always hyperbolic. That applies in particular also in
the case of an IOL according to the invention which has only one convex
surface. If for example an IOL with a 20 dpt refractive power, a refractive
index of 1.46 and a parameter p = 12.3578 mm is selected, which is
dimensioned for the case of a cornea with a 43 dioptres surface refractive
power and an asphericity asph~ _ -0.26, the asphericity of both surfaces of
a biconvex mirror-symmetrical IOL asph~ _ -6.24. In the case of an IOL
whose entry surface is aspherical and whose exit surface is spherical, the
asphericity of the one surface in contrast is asph~ _ -13.9. The asphericity
in the case of an IOL with only one hyperbolic-aspherical surface is in that
case always greater than in the case of a symmetrical IOL. The asphericity
values shown in Figures 4 and 5 represent minimum values in that sense.
In all cases accordingly the asphericity of at least one of the refractive
surfaces of the IOL according to the invention, with a refractive power in
the immersion medium of DI > +3 dpt, is less than -1. In other words the
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topography of at least one of the refractive surfaces can always be
described by a hyperboloid.
It can also be seen from Figures 4 and 5 that such an IOL refracts an
incoming plane wave into an outgoing wave with a hyperbolically curved
wave front for the asphericity of the outgoing wave asphouT is in any event
below -1. That applies both in the environment of the immersion medium
with a refractive index nI = 1.336 (upper curves) and also in air with a
refractive index n~ = 1 (central curve). Preferably the hyperbolic wave front
has an asphericity asphouT < -5.
A conventional IOL with spherically curved surfaces in contrast has a
positive spherical aberration, that is to say it refracts an incoming wave
with a plane wave front into an outgoing wave with an elliptically oblongly
curved wave front. That basically applies in regard to the positive refractive
power of the lens, that is to say both in air and also in the immersion
medium, insofar as the refractive index of the lens material is greater than
that of the environment medium, with a refractive index of the lens
material of 1.46 in particular therefore also in the immersion medium.
By virtue of a measurement of the waveform of the outgoing wave,
with a known refractive index therefore, an IOL according to the first
2o embodiment of the present invention can be distinguished from an
intraocular lens according to the state of the art when it is illuminated with
a plane wave. And more specifically suitable measurement can be effected
in vitro in a standardised measuring structure and does not need to be
implemented in the human eye. An example of such a measuring structure
is shown in Figure 6. It essentially corresponds to a structure 610 known
from the ISO standard 11979-2, comprising an arrangement of optical
elements for producing a plane wave, that is to say for producing and
collimating a parallel beam with which an IOL 614 to be measured is
illuminated. Disposed downstream thereof in the beam direction is a wave
3o front analyser in accordance with Hartmann-Shack 620, for determining the
waveform of the outgoing wave produced by the IOL 614. The wave front
analyser breaks down the beam 616 coming from the IOL by means of a
lens arrangement 622 into a plurality of beams 624 whose local distribution
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is detected by means of a light detector 626, such as for example a CCD
camera. Conclusions about the waveform can be drawn in known manner
on the basis of the distribution, by means of an image evaluation device
(not shown). The imaging properties of the IOL to be investigated can be
determined with that method. The results admittedly do not allow clear
conclusions about the material properties and the topographical parameters
of the intraocular lens as the same imaging properties can be achieved by
intraocular lenses with different refractive indices and surface curvatures.
However, in investigating the IOL, it is precisely the optical properties
thereof that are important so that this method can be universally employed
in comparison with known methods in which evaluation is based on the
topography of spherical lenses and which are therefore not suitable for
measurement of the IOL according to the invention. Accordingly this
measurement method is suitable in particular for distinguishing an IOL
according to the invention from a conventional spherical IOL since, as
indicated hereinbefore, it differs precisely by virtue of its characteristic
imaging properties. Measurements in respect of the imaging properties of
the IOL to be measured can preferably be implemented with this
measurement structure in the ambient medium air, but also in the
immersion medium.
In both of Figures 4 and 5 the refraction properties for intraocular
lenses are selected with refractive powers in the range between 3 dpt and
35 dpt. The intraocular lenses according to the invention however are not
limited to those refractive powers. Higher refractive powers can equally be
selected and can be easily extrapolated on the basis of the steady
configuration of the curves. The foregoing considerations were by way of
example in respect of an IOL with a refractive index of 1.46, a diameter of
6 mm and an axis-parallel edge thickness of 0.25 mm. The invention
however is not limited to an IOL with the stated values for the refractive
index, diameter or edge thickness.
The IOL in accordance with a second embodiment of the present
invention has a central refractive power in the immersion medium DI of a
maximum of -2 dpt. Such an IOL according to the invention also refracts
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an incoming wave with an elliptically oblongly curved wave front into an
outgoing spherical wave, with suitable curvature for the lens surface, that is
to say with a refractive power which decreases towards the lens edge
(negative spherical aberration). Such a lens according to the invention
converts an incoming plane wave into an outgoing wave with an elliptically
oblongly curved wave front.
As already mentioned a conventional spherical lens of positive
refractive power converts an incoming plane wave into a wave with an
elliptically oblongly curved wave front, that is to say the refracted edge
beams experience greater deflection than the central beams. In other
words spherical lenses with a positive refractive power have a positive
spherical aberration. Accordingly, aberration is negative in the case of a
spherical lens with negative refractive power. Such a lens converts an
incoming plane wave into an outgoing wave with an also elliptically
oblongly curved wave front.
That can be seen from following Table 1 comparing the asphericities
of outgoing waves after refraction of an incoming plane wave by intraocular
lenses which are in accordance with the invention and which are
conventional, each with the same central (nominal) refractive power in
immersion DI both for the environment medium air and also for the
immersion medium.
Table 1
DI of the -2 dpt -4 dpt -7 dpt -10
dpt
IOL (in
immersion
spherical as hour in immersion+27.6 +36.4 +35.9 +35.89
IOL as hour in air +3.55 +3.63 +3.63 +3.65
IOL asphouT in immersion+44143 +7321 +1521.3 +559.4
according
to the asphour in air +1807.9 +302.49 +64.03 +23.9
invention
In accordance with the data assembled in Table 1 the wave fronts
measured in the immersion medium, in investigation of the IOL according
to the invention, have a positive asphericity which is 1600 to 20 times
greater in comparison with a conventional spherical IOL, in each case in
dependence on the refractive power of the lenses. In the case of refraction
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in air the wave fronts produced by the IOL according to the invention, in
comparison with the wave fronts produced by a conventional spherical lens,
have a positive asphericity which is increased by 500 to 8.5 times, once
again dependent in each case on the refractive power of the lenses. In
particular the asphericity of a spherical IOL with negative refractive power
in air, independently of the magnitude thereof, does not reach any values
which are greater than +10. The two outgoing waves can therefore be
easily distinguished by measurement of their asphericity. With the
refractive power of the lenses being known therefore once again it is
1o possible by means of the apparatus shown in Figure 6 to distinguish
whether the lens being investigated is a conventional spherical IOL or an
IOL according to the invention.
An intraocular lens according to a third embodiment of the present
invention has a central refractive power of between +2 dpt and -1 dpt in
the immersion medium. In this case also the refractive power of the IOL
according to the invention is lower at the edge than at the centre. Figure 7
shows by way of example a symmetrical IOL 700 with a refractive power at
the centre of +2 dpt, in cross-section. The lens 700 is designed to convert
an incoming wave from the cornea with a wave front of elliptical asphericity
2o asphlN = 5.51 into a substantially spherical wave. It will be seen that the
meridian of the apex surface 710 of that IOL has an inflexion point 712 at a
maximum spacing of about 1.8 mm from the central axis 714 of the lens.
Figures 8 and 9 show the configuration of the wave fronts of
outgoing waves, which are produced by the IOL according to the invention
on the one hand and a spherical IOL with the same nominal refractive
power on the other hand, when a plane wave is introduced. It can be seen
in the comparison that the meridian of the wave front produced by the IOL
according to the invention has an inflexion point whereas the wave front
produced by a conventional lens extends monotonically. That applies both
3o in the environment medium air, see Figure 8, and also in the immersion
medium, see Figure 9. In that way it is also possible to clearly distinguish
lenses according to the invention with the above-mentioned refractive
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power from conventional, spherically curved lenses, by the method
described with reference to Figure 6.
